Summary

Zusammenfassung Überblick Parablen

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Course
Mathematik

Institution
Gymnasium

In meiner Zusammenfassung wird einfach das Thema Parabeln, Potzenfunktionen und Wurzelfunktionen erklärt. Mit diesem Lernzettel ist man perfekt für die Arbeit in der 11. Klasse vorbereitet.

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Uploaded on October 30, 2024
Number of pages 4
Written in 2023/2024
Type Summary

quadratische gleichungen
quadratische funktionen
parabeln
potenzfunktionen
wurzelfunktionen
nullstellen
transformationen

Institution Secondary school
Education Gymnasium
Course
Mathematik
School year 1

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Mathe Ka 2

Quadatische Gleichungungen
P-Q Formel Punktprobe
x + p +
q
= 0 meist muss man den x-Wert noch 1 .
X-Wert einsetzen

x(x
= -

E =
(8) g -
in eine Gleichung einsetzen um den 2 .

4-Wert mit Wert aus dem Punkt vergleichen
Xy =
Xz = Punkt zu vervollstndigen BSD .
A(7123) B(41-14)

A(l) B) I) y
= 3 7 .
+ 2 y = 3 4 .
+ 2

23 14
y y
= =

A: liegt aufg A :
liegt nicht auf g

Schnittpunkte
. Nullstellen
1 (mit der X-Achse) 2) Nullstelle (mit der y-Achsel
0 X 0
y
= =

y
= 3x - 9 N(310)
y
= = x + 3 P(OB)
0 3x- 9 Punkt einsetzen !
=3
= (+9 0+
Y
9 3x 1 :3 Durch die O fallt es und bleibt nur noch
weg es c
=

3 X 3
y
= =

Quadratische Funktionen (Parabeln)

Nullstellen
Eine quadratische Funktion ist eine Funktionsgleichung >
-

Stellen an denen der Graph die x-Achse schneidet
in der Form f(x) ax + x
=
+c
. .
1 Funktionen der Form f(x) ax +
=
C . Funktion der Form f(x)
2 = ax + by
↑
Hauptform BSp f(x) 2x2
Die Graphen 1 f(x) 3x2 + 48 + 18
quadratischer
2
Bsp
=

Funktionen
=

f(x) xi 7x
. .
:
.

= -

,

0 = -
3x2 + 481-48 0 =
2x2 + 181 18 -

heisen Parabeln . 0 = x2 -
7x
-
48 = -
3X
2
1 : ( - 3) -
18 =
2x2 1: 2

Scheitelform-fXYyVerschie
as 0 =
x .
(x- 7) Ausklammern
16 x2 It 0 x2
4
= - =

Y-Achse

X- Achse
14 =
x
SatzvomNullprodukt := O oder x- 70 1

N- ( 410)
-

Nz(410) xz = 7

Scheitelpunkt setzt sich wie
folgt zusammen : S(xslys)
- (010)
N N2(710)

Produktform - f(x) =
a(x x)(x xe)
-
- . Funktionen der Form f(x) ax" + by + c
3 =

nur mglich wenn Funktion Nullstellen hat
Bsp : f(x) = 2x2 -
8x + 6

0 = 2x2 -
8x + 61 : 2

=

0 xz -
(x + 3

=
= 23
=
2= M

=
2= 1

xy =
3Xz = 1

N + (310) N2(110)
~

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